Question

Find the limits for integrating f (x, y) over the region D using polar coordinates.

Answer 1

(a) The integral is

(b) The line y = √2 in polar coordinates is given by

It intersects the circle in the point √2,√2 , which corresponds to θ = π/4 . Therefore the integral is

(c) The line x = √3 in polar coordinates is given by

and the hypothenuse of the triangle has slope 1/ √3 , which corresponds to θ = π/6 . Therefore the integral is